Stitz-Zeager_College_Algebra_e-book

If we reect across the x axis and then the y axis we

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Unformatted text preview: pretend the y -axis is a mirror, the reflection of (−2, 3) across that axis would be (2, 3). If we reflect across the x-axis and then the y -axis, we would go from (−2, 3) to (−2, −3) then to (2, −3), and so we would end up at the point symmetric to (−2, 3) about the origin. We summarize and generalize this process below. Reflections To reflect a point (x, y ) about the: • x-axis, replace y with −y . • y -axis, replace x with −x. • origin, replace x with −x and y with −y . 1.1.1 Distance in the Plane Another important concept in geometry is the notion of length. If we are going to unite Algebra and Geometry using the Cartesian Plane, then we need to develop an algebraic understanding of what distance in the plane means. Suppose we have two points, P (x1 , y1 ) and Q (x2 , y2 ) , in the plane. By the distance d between P and Q, we mean the length of the line segment joining P with Q. (Remember, given any two distinct points in the plane, there is a unique line containing both points.) Our goal...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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